Electriclly Tunle g ctors in Quntum Dot Moleculr Spin Sttes M.. Doty,, * M. Scheiner, I. V. Ponomrev, E. A. Stinff, A. S. Brcker, V. L. Korenev, 2 T. L. Reinecke, nd D. Gmmon Nvl Reserch Lortory, Wshington, D.C. 2375, USA 2 A.. Ioffe Physicl Technicl Institute, St. Petersurg 942, Russi (Received 4 August 26; pulished Novemer 26) We present mgnetophotoluminescence study of individul verticlly stcked InAs=GAs quntum dot pirs seprted y thin tunnel rriers. As n pplied electric field tunes the reltive energies of the two dots, we oserve strong resonnt increse or decrese in the g fctors of different spin sttes tht hve moleculr wve functions distriuted over oth quntum dots. We propose phenomenologicl model for the chnge in g fctor sed on resonnt chnges in the mplitude of the wve function in the rrier due to the formtion of onding nd ntionding oritls. DOI:.3/PhysRevLett.97.9722 PACS numers: 75.4.G, 78.2.Ls, 78.47.+p, 78.67.Hc Quntum dots nd quntum dot molecules (QDMs) hve proven to e verstile medium for isolting nd mnipulting spins [,2], which re of gret interest for quntum informtion processing [3,4]. In prticulr, photoluminescence (PL) spectr hve een used in self-ssemled QDMs to oserve coherent tunneling [5 8] nd identify spin interctions through fine structure [9]. Electricl control of isolted spins through their g fctors is highly desirle for implementtion of quntum gte opertions. To dte, electricl control of g fctors hs only een oserved in ensemles of electrons in quntum wells y shifting the electron wve functions into different mterils [ 3]. In this Letter we present striking electric field resonnce in the g fctor for moleculr spin sttes confined to single quntum dot molecule. To our knowledge this is the first oservtion of electricl control over the g fctor for single confined spin. Moreover, the isoltion of single QDM llows us to spectrlly resolve nd identify individul moleculr spin sttes tht hve different g fctor ehviors. In ig. () we indicte moleculr spin sttes of oth the neutrl exciton (X, one electron recomining with one hole) nd positive trion (X, electron-hole recomintion in the presence of n extr hole) t zero mgnetic field. The different electric field dependences of the g fctors for these sttes is pprent in ig. (), where the splitting of PL lines increses for some moleculr spin sttes nd decreses for others. This electric field dependence is nerly n order of mgnitude lrger thn previously reported in quntum wells [ 3]. The effect rises from the formtion of onding nd ntionding oritls, which results in chnge in the mplitude of the wve function in the rrier t resonnce. Our QDMs consist of two verticlly stcked selfssemled InAs dots truncted t thickness of 2.5 nm nd seprted y 2 nm GAs tunneling rrier [4]. As n pplied electric field tunes the reltive energies of the two dots, strong tunnel coupling etween the hole sttes cretes the moleculr spin sttes. Unlike smples with thicker tunnel rrier [5], the sttes retin moleculr chrcter throughout the oserved rnge of electric fields. We present dt from single molecule, ut the universlity of the ehvior hs een verified y detiled studies of 7 other molecules from the sme smple. We first explin the spectr nd moleculr spin sttes t B T. We then descrie the mgnetic field dependence nd propose phenomenologicl model for the electric field-dependent Zeemn splitting. In ig. 2 we show ll PL lines from X nd X t B T. These lines re identified y their reltive energies, the power dependence of their intensities nd the electric field dependence of the nticrossings [5]. The X lines [ig. 2()] show cler nticrossing t X. The nticrossing rises from tunnel coupling etween the ground stte hole levels in ech dot, which forms onding (XB ) nd ntionding (XA ) oritls. The electron remins in the ottom dot throughout the rnge of electric fields considered here [5]. The X lines [ig. 2()] hve more com- 298 296 B = B = 6 IG. (color online). () B Tphotoluminescence spectr of single QDM. The complex pttern of nticrossings rises from the formtion of moleculr spin sttes. () At B 6T, the moleculr spin sttes hve Zeemn splitting (rs) tht depends strongly on the pplied electric field (). 3-97=6=97(9)=9722(4) 9722-26 The Americn Physicl Society
Report Documenttion Pge orm Approved OMB No. 74-88 Pulic reporting urden for the collection of informtion is estimted to verge hour per response, including the time for reviewing instructions, serching existing dt sources, gthering nd mintining the dt needed, nd completing nd reviewing the collection of informtion. Send comments regrding this urden estimte or ny other spect of this collection of informtion, including suggestions for reducing this urden, to Wshington Hedqurters Services, Directorte for Informtion Opertions nd Reports, 25 Jefferson Dvis Highwy, Suite 24, Arlington VA 2222-432. Respondents should e wre tht notwithstnding ny other provision of lw, no person shll e suject to penlty for filing to comply with collection of informtion if it does not disply currently vlid OMB control numer.. REPORT DATE AUG 26 2. REPORT TYPE 3. DATES COVERED --26 to --26 4. TITLE AND SUBTITLE Electriclly Tunle g ctors in Quntum Dot Moleculr Spin Sttes 5. CONTRACT NUMBER 5. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERORMING ORGANIZATION NAME(S) AND ADDRESS(ES) Nvl Reserch Lortory,4555 Overlook Avenue SW,Wshington,DC,2375 8. PERORMING ORGANIZATION REPORT NUMBER 9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES). SPONSOR/MONITOR S ACRONYM(S) 2. DISTRIBUTION/AVAILABILITY STATEMENT Approved for pulic relese; distriution unlimited 3. SUPPLEMENTARY NOTES 4. ABSTRACT. SPONSOR/MONITOR S REPORT NUMBER(S) 5. SUBJECT TERMS 6. SECURITY CLASSIICATION O: 7. LIMITATION O ABSTRACT. REPORT unclssified. ABSTRACT unclssified c. THIS PAGE unclssified Sme s Report (SAR) 8. NUMBER O PAGES 4 9. NAME O RESPONSIBLE PERSON Stndrd orm 298 (Rev. 8-98) Prescried y ANSI Std Z39-8
3 296 292 B plicted pttern ecuse nticrossings occur in oth the initil (one electron nd two holes) nd finl (one hole) sttes [5,9]. To explin the origin of the X moleculr spin sttes we turn to the Hmiltonins. The sis sttes will e identified s e B;e T h B ;h T X Q k, where e B [e T ] re the spins of electrons ( =2: " or # ) nd h B [h T ] the spins of hevy holes ( 3=2: * or + ) in the ottom [top] dot. X indictes n exciton (h single hole) nd Q is the net chrge. k is the totl spin projection. Singlets, which hve totl spin =2, will e denoted X S to distinguish them from the =2 triplets. The finl stte hs only single hole with reltive energies given y the digonliztion of the Hmiltonin: ^H h t h () t h e~d in the spin-degenerte ; *; h 3=2, ; ;* h 3=2 sis, where t h is the tunneling energy for re hole, ~d is the distnce etween dot centers nd is the pplied electric field. The energies of the finl sttes s function of electric field re shown in ig. 3(). The formtion of onding nd ntionding sttes t the nticrossing point is illustrted. The initil stte (X ) contins one electron nd two holes. or simplicity we present only the electron-spin-up cse, which is degenerte with the spin-down cse t zero mgnetic field. If oth holes re in the sme dot, the Puli principle requires singlet configurtions: " ; *+; X S (oth in the ottom dot) or "; ;*+ X S (oth in the top dot). If there is one hole in ech dot, singlet ( "; +;* X S ) nd triplet ("; +;* X =2, "; +;+ X 5=2, "; *;* X "; 7=2 ) configurtions re possile. By +;* X S we men the ntisymmetric hole spin wve function ( +, * *, + ). "; +;* X =2 T IG. 2 (color online). Energies extrcted from ig. (). () X lines nticross t X, where the direct (lower inset) nd indirect (upper inset) trnsitions re degenerte. () X initil sttes nticross t X nd ner 9 kv=cm. inl (hole) sttes nticross t h. Inset: chrge distriution for the circled singlet nd triplet trnsitions. mens the symmetric hole spin wve function ( +, * *, + ). The reltive energies of the initil sttes re given y the Hmiltonin 9722-2 2 2 GAs GAs IG. 3 (color online). Clculted zero mgnetic field energies of spin-degenerte () initil sttes (X ) nd () finl sttes (h ) [24]. Lels indicte the dominnt sis stte for esy comprison to Eq. (2). Insets in () show the onding (lower) nd ntionding (upper) wve functions (green) nd proility distriutions (red). (c) ine structure of singlet nd triplet sttes t 79:2 kv=cm. Arrows indicte opticlly llowed trnsitions to the onding finl stte. t X t X e~d J eh t X J ^H X E =2 B E 5=2 @ C E 7=2 A t X 2e~d 2 (2) in the " ; *+; X S, "; +;* X S, "; +;* X =2, "; +;+ X 5=2, "; *;* X 7=2, "; ;*+ X S sis. nd 2 re due to Coulom interctions, t X is the Coulom-corrected tunneling energy for hole in the presence of n electron nd dditionl hole, E k e~d mj eh with m,, for k =2, 5=2, 7=2. J eh is the exchnge energy etween n electron nd hole in the sme dot [5,5]. Digonlizing Eq. (2) gives the energies of the initil sttes, which re plotted s functions of electric field in ig. 3(). Becuse tunneling is spin conserving process, only the "; +;* X S singlet stte cn tunnel couple with " ; *+; X S nd "; ;*+ X S, which must e singlets ecuse the two holes re in the sme dot. These 3 singlets re therefore strongly mixed to crete moleculr oritl sttes tht nticross ner 57 kv=cm ( X ) nd 9 kv=cm. Unlike the singlet sttes, the triplet sttes do not mix nd re not ffected y these nticrossings [6]. This cretes kinetic splitting etween triplet nd singlet sttes [7]. An exmple is indicted y the dshed ovl in ig. 2(), where the lower energy singlet line remins seprted from the two opti- c
clly llowed triplet lines, which re split y electron-hole exchnge. The fine structure of the corresponding sttes is shown in ig. 3(c). By dding the Zeemn interction to the Hmiltonin [8], we clculte the mgnetic field dependence of the moleculr spin sttes. igure 4() shows the sttes of ig. 3(c), which split into doulets with n pplied longitudinl mgnetic field. The finl sttes re simply the two spin orienttions of single hole, split y g h. The splitting of initil sttes depends on their spin configurtion. Becuse of the two prllel hole spins, X 5=2 hs lrge splitting given y g e 2g h while X 7=2 is split y g e 2g h. In contrst, the =2 singlet (XS ) nd triplet (X =2 ) hve oppositely pired hole spins nd therefore smll splitting given y g e. The g fctor for PL trnsitions is given y the difference in g fctor etween the initil nd finl sttes. Awy from the electric field resonnces, the g fctor is g T g e g h, s indicted y the verticl lines. Using the model descried elow, we otin g T 2:2. To plot the initil nd finl sttes in ig. 4() we hve tken the reltive weights of the electron nd hole g fctors to mtch those otined y Byer: g e :6nd g h :6 [8]. The clculted energies of the trnsitions re shown y the lines in ig. 4(). The experimentlly oserved PL energies re given y the symols, with the dimgnetic shift (:9 ev=t 2 ) sutrcted. The g-fctor resonnces re clerly evident in ig. 5, where the symols plot the mesured energy splitting of the X nd two X Zeemn doulets t B 6T s function of electric field. Strong enhncement or suppression of the splitting is oserved t h nd X. All of the 2 297. 296.5 296. 295.5 2 3 4 5 6 Mgnetic ield (T) IG. 4 (color online). () Mgnetic field dependence of initil (X ) nd finl (h) sttes for the singlet nd triplet trnsitions t n electric field of 79:2kV=cm [schemtic ig. 3(c)]. Verticl lines indicte spin llowed recomintions. () Clculted (colored lines) nd experimentlly oserved (lck points) PL energies. (c) Zeemn splitting of PL lines ( ) nd initil nd finl sttes for X 5=2 (red lines) nd X S (green lines). c 9722-3 dt cn e qulittively explined y phenomenologicl model of the formtion of onding nd ntionding oritls, which results in resonnt chnges in the mplitude of the wve function in the rrier. We focus first on trnsitions involving onding oritl (open symols), which hve n incresed mplitude of the wve function in the rrier [ig. 3() lower inset]. The wve function for the onding oritl of single hole cn e written s B ji j2i, where ji nd j2i re the sis sttes of Eq. (), the wve functions for holes loclized in the two different dots. The coefficients nd re functions of electric field determined y Eq. (). The electric field-dependent g fctor for hole in onding oritl is given y g B h h Bjg h z j B i, where g h z is the hole g fctor s function of position in the smple. g h z is tken s phenomenologicl prmeter, in prt ecuse the degree of lloying etween the nominlly pure InAs dots nd GAs rrier is unknown [9]. If we ssume tht the g fctors for the holes loclized in ech dot re the sme, we get g B h g h 2g 2, where g 2 hjg h z j2i gives the contriution from the mplitude of the wve function in the rrier. In the cse of the XS singlet [shown in igs. 3(c) nd 4(c)], the initil sttes re split y g e, so the totl trnsition g fctor is given y g B T g e g B h g 2t T h g 2 q ; (3) e 2 ~d 2 h 2 4t 2 h where the explicit form for 2 determines the line shpe centered round the nticrossing point h. The lower lck line in ig. 5 is otined y fitting Eq. (3) to X S. Using the mesured vlues of t h (.86 ) nd h (63:3 kv=cm) we find g 2 :65. The rrier contriution is positive, like the hevy hole g fctor in ulk GAs ( :5) [2,2]. Becuse g T nd g 2 hve opposite sign, the splitting reches minimum t h, where the mplitude in the rrier is t mximum. The g fctor t the minimum is :44. Splitting (µev) 6 2 8 4 4 3 -g T ( ) IG. 5 (color online). Zeemn splitting nd corresponding g fctor, g T, s function of electric field t B 6T. 2
Becuse the 5=2 triplet sttes recomine to the sme onding oritl of the finl hole (ig. 3), the model predicts the splitting of these lines s function of electric field with no dditionl fitting. As shown in ig. 4c, the 5=2 triplet sttes hve n initil stte splitting of g e 2g h. The trnsition g fctor is therefore given y g B T g e 2g h g h 2g 2 g T 2g 2. This is shown y the upper lck line, which mtches X 5=2, the oserved splitting of the 5=2 triplets. The mximum splitting corresponds to g fctor of 4:23. To pply the g-fctor model to the onding oritl of the neutrl exciton [lower rnch ig. 2()] we use the mesured tunneling energy (t X :58 ) nd nticrossing field ( X 82: kv=cm). The lower red line in ig. 5 shows the fit to XB, the Zeemn splitting of PL lines from the onding oritl. We find g 2 :32. The electron-hole Coulom interction is responsile for the difference in tunneling energy nd nticrossing field from the re hole cse nd is lso likely responsile for the difference etween g 2 nd g 2. The g fctor t the minimum is :59. Using this vlue of g 2, the model immeditely explins the increse in splitting for the ntionding oritl [upper rnch ig. 2()], which hs reduced wve function mplitude within the rrier. The g fctor for the ntionding oritl is given y g A T g T 2g 2, which increses in mgnitude t the resonnt field ecuse g T is negtive nd g 2 is positive. This is shown y the upper red line in ig. 5, which mtches XA, the Zeemn splitting for excitonic recomintion from the ntionding oritl. The splitting increses to mximum (g fctor 3:35) t the nticrossing point. The ntionding trnsitions for X show similr ehvior, ut re too wek to otin full resonnce curves. The overll greement etween the model nd experimentl dt is quite good. There re some minor discrepncies, which highlight the need for detiled theory, possily requiring inclusion of excited sttes [22]. However, the greement of the dt with the resonnce linewidths clculted using independently mesured vlues of t X nd t h is strong confirmtion tht the g-fctor dependence does rise from the formtion of onding nd ntionding oritls. or X the g-fctor resonnce rises from the wvefunction of the single hole in the finl stte, while for X the oritl wvefunction of the hole is influenced y the dditionl electron. We lso studied smples in which electrons tunnel through the rrier, with n nticrossing energy ( 2:3 ) comprle to tht of the hole-tunneling smple presented here ( :7 ). This requires thicker rrier ( nm) ecuse of the smller electron effective mss. The electron wve function mplitudes in the rrier should e t lest s lrge s the hole-tunneling cse. However, the electron g fctor in ulk GAs ( :44) [23] is similr to the electron g fctor in InAs quntum dots ( :6) nd ccording to our model the contriution from the rrier should not significntly chnge the electron g fctor. We see no electric field dependence of the g fctor in these electron nticrossing smples. By dding luminum to the rrier, the resonnt contriution to the electron g fctor could e enhnced. We hve presented resonnt chnge in g fctor s function of electric field for the moleculr spin sttes of QDMs with thin tunnel rrier. By studying single QDMs, we re le to identify the individul moleculr spin sttes nd the different resonnt ehvior of their g fctors. The results suggest tht design of moleculr spin sttes nd tunnel resonnces my provide new opportunities for comining opticl nd electricl control of confined spins. We cknowledge finncil support y NSA/ARO, CRD, RBR, RSS, nd ONR. E. A. S., I. V. P., nd M.. D. re NRC/NRL Reserch Assocites. *Electronic ddress: doty@loch.nrl.nvy.mil []. H. L. Koppens et l., Science 39, 346 (25). [2] J. R. Pett et l., Science 39, 28 (25). [3] D. Loss nd D. P. DiVincenzo, Phys. Rev. A 57, 2 (998). [4] R. Vrijen et l., Phys. Rev. A 62, 236 (2). [5] E. A. Stinff et l., Science 3, 636 (26). [6] H. J. Krenner et l., Phys. Rev. Lett. 94, 5742 (25). [7] H. J. Krenner et l., Phys. Rev. Lett. 97, 7643 (26). [8] G. Ortner et l., Phys. Rev. Lett. 94, 574 (25). [9] M. Scheiner et l., cond-mt/6724. [] G. Slis et l., Nture (London) 44, 69 (2). [] M. Poggio et l., Phys. Rev. B 7, 235(R) (24). [2] H. W. Jing nd E. Ylonovitch, Phys. Rev. B 64, 437(R) (2). [3] Y. Lin et l., Physic E (Amsterdm) 2, 656 (24). [4] Dots re MBE grown on GAs [5] in diode structure; n Al msk with m pertures isoltes single QDMs. [5] We cnnot rule out smll direct exchnge energy etween holes in seprte dots, J hh. Becuse the nticrossing ner 9 kv=cm is not fully oserved, we cnnot seprte J hh from the kinetic singlet-triplet splitting due to tunneling. Since the kinetic splitting is dominnt in these smples we hve, for simplicity, tken J hh. [6] The "; +;* X =2 sttes mix slightly with "; +;* X S through electron-hole exchnge, J eh [9]. [7] P. zeks, Lecture Notes on Electron Correltion nd Mgnetism (World Scientific, Singpore, 999). [8] M. Byer et l., Phys. Rev. B 6, 7273 (2). [9] Our vlues of g e :6 nd g h :6 re typicl for InAs QDs. or ulk GAs, g h :5 for hevy holes nd g e :44 [2]. Zeemn splittings for oth electrons nd holes re given y g B B. [2] V. A. Krsyuk et l., Phys. Rev. B 49, 6 38 (994). [2] M. J. Snelling et l., Phys. Rev. B 45, 3922(R) (992). [22] There is evidence tht the first excited hole stte is 7 higher in energy. ( 6 kv=cm). [23] H. Kosk et l., Electron. Lett. 37, 464 (2). [24] Numericl vlues from experimentl spectr: 3:2, 2 3:, t h :86, t X :24, J eh :6, ~d 4:29 nm. 9722-4